...Archimedes was a mathematician, but he was so much more. He is known for his opulent contributions to the fields of mathematics, geometry, physics, and hydrostatics. To illustrate Archimedes’s genius you can simply take a look at some of his inventions. Archimedes was a mastermind of mathematics. One of his biggest accomplishments is approximating pi, he did this by utilizing the technique known as the method of exhaustion. His approximation is still used today. He also proved that the area of a circle was equal to pi multiplied by the square of the radius of the circle. He also discovered what is called Archimedes Principle, a principle relating buoyancy to displacement. He considered his most important discoveries his discoveries on the sphere and cylinder. He realized that the volume of a cylinder is equal to 2/3 times the volume of the corresponding sphere and that the surface area of cylinder, including both ends, equals 2/3 times the surface area of the corresponding sphere. Archimedes also worked on the quadrature of the parabola, conoids and spheroids and found that the area of the parabolic segment of a parabola is equal to 3/4 times that of the triangle with the same base and height, the volume of any segment of a paraboloid is 3/2 times that of a cone with the same base and axes, and the ratio of the two segments formed by cutting a solid bounded by a paraboloid with two planes in an arbitrary way is equal to that of the squares of the lengths of their axes. He created...
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...the Colosseum, Teotihuacán and the cities and pyramids of the Mayan, Inca and Aztec Empires, the Great Wall of China, the Brihadeeswarar Temple of Thanjavur and tombs of India, among many others, stand as a testament to the ingenuity and skill of the ancient civil and military engineers. The earliest civil engineer known by name is Imhotep.[3] As one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser (the Step Pyramid) at Saqqara in Egypt around 2630-2611 BC.[6] Ancient Greece developed machines in both civilian and military domains. The Antikythera mechanism, the first known mechanical computer,[7][8] and the mechanical inventions of Archimedes are examples of early mechanical engineering. Some of Archimedes' inventions as well as the Antikythera mechanism required sophisticated knowledge of differential gearing or epicyclic gearing, two key principles in machine theory that helped design the gear trains of the Industrial Revolution, and are still widely used today in diverse fields such as robotics and automotive engineering.[9] Chinese, Greek and Roman armies employed complex military machines and inventions such as artillery which was developed by the Greeks around the 4th century B.C.,[10] the trireme, the ballista and the catapult. In the Middle Ages, the trebuchet was developed. Engineers apply mathematics and sciences such as physics to find suitable solutions to problems or to make improvements to...
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...Alexander the Great, king of Macedonia, ruled an empire that stretched from the Balkans to the Himalayas and from Egypt to the Caspian Sea during the mid-4th century BC. But his empire soon fell apart after his sudden and unexpected death in Babylon. His goal of further conquest was thus cut short, and his empire was left without a successor. What Alexander left behind was not a huge empire, but the spread and intermingling of ideas among the areas he conquered. Some important advancement in medicine and science were thus made, owing to the collaborative work of many Hellenistic intellectuals from Alexander’s former empire. The source of Greek knowledge about medicine came from Egypt, which was fairly well-developed by the Greece was entering its Golden Age. Greek figures such as Pythagoras traveled widely, and picked up discoveries from places and brought them back to Greece. Thales gained first-hand experience of medicine when he was training in Egypt. Similar to Greek medicine, Egyptian medicine also lied in religion and spirituality. The Egyptian god of medicine was Imhotep, whose role was analogous to that of Asclepius. People would pray to him and other gods for healing, and it was believed that gods played a role in matters of health and disease. Despite these religious origins and beginnings, Egyptian medicine was rather rational and scientific. Blood was thought to be an important nutritive and regulatory substance, and the heart was considered to be the center of the...
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...The Ancient Greeks developed astronomy, which they treated as a branch of mathematics, to a highly sophisticated level. The first geometrical, three-dimensional models to explain the apparent motion of the planets were developed in the 4th century BC by Eudoxus of Cnidus and Callippus of Cyzicus. Their models were based on nested homocentric spheres centered upon the Earth. Their younger contemporary Heraclides Ponticus proposed that the Earth rotates around its axis. A different approach to celestial phenomena was taken by natural philosophers such as Plato and Aristotle. They were less concerned with developing mathematical predictive models than with developing an explanation of the reasons for the motions of the Cosmos. In his Timaeus, Plato described the universe as a spherical body divided into circles carrying the planets and governed according to harmonic intervals by a world soul. Aristotle, drawing on the mathematical model of Eudoxus, proposed that the universe was made of a complex system of concentric spheres, whose circular motions combined to carry the planets around the earth. This basic cosmological model prevailed, in various forms, until the 16th century AD. In the 3rd century BC Aristarchus of Samos was the first to suggest a heliocentric system, although only fragmentary descriptions of his idea survive. Eratosthenes, using the angles of shadows created at widely separated regions, estimated the circumference of the Earth with great accuracy. Greek...
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...Friday, December 13 4:23 PM eschulte account log off PHYS 101 Exams UIUC Instructor Unit 3: Homework / Homework / Homework / Schulte, Elaine Student Homework: Hour Exam 3 Deadline: 100% until Thursday, November 21 at 8:00 AM Problems Print Assignment View Standard Exercise The Mass and The Spring 1 2 3 The Mass and The Spring Standard Exercise The Pendulum Standard Exercise The Hydraulic Lift Standard Exercise Archimedes and the King's Crown Standard Exercise The Garden Hose Standard Exercise The Guitar String A block of mass m = 5 kg is connected to a vertical spring as shown in the diagram. When the mass is at rest, the spring stretches y0 = 5 cm beyond its natural length lspring = 14 cm. Standard Exercise The Intense Speakers 1) For this system, in the vertical configuration, y0 = 5 cm gives the equilibrium position. False True Submit Hide Solution Standard Exercise The Speeding Car Standard Exercise Heating a Metal Strip Solution: This question asks about the effect of gravity on the equilibrium position of a spring. Remember that the effect of a gravitational force is to stretch the spring an amount Δx = mg/k. This stretch in the spring represents an offset in the natural (horizontal) equilibrium position of the spring. While the question is strangely worded, the answer is true, the change in position y0 = 5 cm represents the new equilibrium position. Standard Exercise Compressing...
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...ARCHIMEDES' PRINCIPLE * Thilan vimukthi rathnayake.(100037574) * Nuwantha wijayaratne.(100038234) * Mewan weerasekara. (100037930) * Madhawa udawattha.(100038140) AIM Our first aim of this experiment is to find densities of aluminium and wood by measuring the volume and its weight. Secondly, we used Archimedes principle ( when a body partly or totally immense in a fluid the buoyant force is equal to the weight of liquid that displaced by the fluid) to find the densities of wood(pw) and aluminium(pAl). APPARATUS 1. Aluminium block. 2. Wood block. 3. Spring balance (0-1.0N). 4. Digital top-pan balance. 5. Reel of cotton. 6. Small beaker. 7. Ruler. 8. Scissors. METHOD We used two methods to determine the densities of wood and aluminium. For the both methods we have measured the masses of wooden block(Mw) and aluminium block(MAl). * Method one We measured the lengths of wooden(Lw) and aluminium(LAL) to calculate the volume of two blocks. We then took lengths of every sides to reduce the error coursing by manufacturing. Then we calculate the density of two blocks. * Method two 1. Firstly, we measured the weight of aluminium block when it suspended in air by using spring balance. Thereafter we let it fully immerse in water and calculate weight of it. 2. Secondly, we measured weight of wooden block using spring balance and let it float on water, wooden block was partly immersed in we took height above surface...
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...Discussion: This lab experiment consisted in locating the metacentric point in order to test the buoyancy stability of a lab pontoon under certain circumstances. The metacenter is the point of intersection of the buoyant force and the center of gravity. In order to verify the stability conditions of an immersed body is necessary to locate its metacentric point. One of the conditions is that when the center of buoyancy and center of gravity are coincident, the body is stable. In this experiment the center of gravity was higher than the center of buoyancy causing a slight tilt when changing the position of mass, although it became unstable as the experiment carried on, it still was stable enough to produce a moment to counter the action as the metacenter increases. When the center of gravity is above the center of buoyancy, the location of metacentric Height is lower. In our experiment everytime there was a change on the position of mass that would increase the angle of tilt, the metacentric height and the position of mass would move to more than 0.05 m ,thus the metacentric height would be increase, however the possibility for the pontoon to tip would also increase significantly. ● Conclusion: The apparatus remained stable throughout the experiment. Data recorded for the metacentric point was obtained from theoretical and experimental formulas using two different centers of gravity, 0.075 m and 0.125 m. Although the position of mass changed with each trial...
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...Archimedes of Syracuse is quite easily one of the greatest scientists, if not the greatest scientist to ever walk this earth. He is one of the greatest scientists because of the things that he discovered at such an early time (287 BC – 212 BC). They are still important and relevant today for modern science, and even 1800 years after Archimedes had died they were important for Newton. Archimedes has made so many major contributions to our understanding of science that scientists still can’t believe he did all of them. One of the many major contributions he made to physics was that he discovered the laws of levers and pulleys, which allow us to move heavy objects using small forces. This was a very important discovery because even though we may not realize it there are inventions around us that are invented because of Archimedes. An important example of a lever is something as simple as a wheel barrel, we lift it up and apply force and suddenly the load feels lighter because of the fulcrum (pivot). Archimedes also discovered one of the most fundamental discoveries of physics which was the center of gravity. The understanding of center of gravity is extremely important for things such as objects to remain stable. Race cars have a low center of gravity which makes them more stable, compared to a monster truck which has a high center of gravity and ultimately gives it a higher chance of rolling and lowers there stability. Archimedes wasn’t done with these discoveries that are fundamental...
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...The move towards a rational understanding of nature began at least since the Archaic period in Greece (650 BCE – 480 BCE) with the Pre-Socratic philosophers. The philosopher Thales (7th and 6 centuries BCE), dubbed "the Father of Science" for refusing to accept various supernatural, religious or mythological explanations for natural phenomena, proclaimed that every event had a natural cause.[2] Thales also made advancements in 580 BC by suggesting that water is the basic element, experimenting with magnets and attraction to rubbed amber, and formulating the first cosmologies. Anaximander, famous for his proto-evolutionary theory, disputed the ideas of Thales and proposed that rather than water, a substance called apeiron was the building block of all matter. Heraclitus (around 500BC) proposed that the only basic law governing the universe was the principal of change and that nothing remains in the same state indefinitely. This observation made him one of the first scholars in ancient physics to address the role of time in the universe, one of the most important concepts even in the modern history of physics. The early physicist Leucippus (first half of 5th century BCE) adamantly opposed the idea of direct divine intervention in the universe, instead proposing that natural phenomena had a natural cause. Leucippus and his student, Democritus, were the first to develop the theory of atomism – the idea that everything is composed entirely of various imperishable, indivisible elements...
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...ESTABLISHING THE STRESS LOADING THE ELEMENTS [pic] Fig. 1.1 2. MAIN SCREW CALCULUS 2.1. CHOOSING THE MATERIAL It is chosen OL 50 STAS 500/2 [3] PRE-DIMENSIONING CALCULUS The calculus load F= Q·ctgαmin αmin= 30º [pic] Fig. 2.1 F= Q·ctgαmin= 8914·ctg30°= 15439.5 N Calculus of the load Fc, N Fc= β·F= 1.3·15439.5= 20071.3 N β= 1.25 ... 1.3 [3] The thread's inner diameter [pic] [pic] [pic]=100 ... 120 Mpa [3] Choosing the thread It is chosen Tr 20X4 with the dimension in table 24.2 Table 2.1 |Nominal diameter |Pitch |Medium diameter |External diameter |Inner diameter | |d, mm |P, mm |d2=D2,, mm |D4, mm | | | | | | | | | | | | | |D3, mm |D1,mm | |20 |4 |18 |20.5 |15.5 |16 | CHECKING THE SELF-BRAKING CONDITION The thread's declination...
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...LAB #1 Laboratory Techniques and Measurements Ashley Izor CHML115 01-07-16 Data Table 1: Length measurements. Data Table 1: Length measurements. | Object | Length (cm) | Length (mm) | Length (m) | CD or DVD | 19cm±1cm | 190mm±1mm | 0.19m | Key | 5.2cm±0.1cm | 52mm±0.1mm | 0.052m | Spoon | 18.9cm±0.1cm | 189mm±0.1mm | 0.189m | Fork | 21cm±1cm | 210mm±1mm | 0.21m | Data Table 2: Temperature measurements. | Water | Temperature (°C) | Temperature (°F) | Temperature (K) | Hot from tap | 48°C±1°C | 118.4°F±1°F | 321.15K | Boiling | 99°C±1°C | 210.2°F±1°F | 372.15K | Boiling for 5 minutes | 104°C±1°C | 219.2°F±1°F | 377.15K | Cold from tap | 20°C±1°C | 68°F±1°F | 293.15K | Ice water – 1 minute | 5°C±1°C | 41°F±1°F | 278.15K | Ice water – 5 minutes | 1°C±1°C | 33.8°F±1°F | 274.15K | Data Table 3: Mass measurements. | Object | Estimated Mass (g) | Actual Mass (g) | Actual Mass (kg) | Pen or pencil | 5g | 5g | 0.005kg | 3 Pennies | 2.5g | 7.5g | 0.0075kg | 1 Quarter | 2.5g | 5.7g | 0.0057kg | 2 Quarters, 3 Dimes | 17.5g | 18.1g | 0.0181kg | 4 Dimes, 5 Pennies | 16g | 21.6g | 0.0216kg | 3 Quarters, 1 Dime, 5 Pennies | 27.5g ...
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...Opening a bottle of wine with corkscrew Instructions: 1. Cut the foil off. • Cut around the underside of the lip of the bottle to ensure no wine will touch the foil. 2. Unfold corkscrew and insert it into the cork. • Position the tip of the corkscrew in the centre of the wine bottle's cork, push it in, and begin twisting. Keep twisting the corkscrew until you have only one twist left. • Don't twist too far into the cork, or pieces from the bottom of the cork may get dislodged into the wine. • If you don't twist far enough, the cork may break in two when you try to extract it. 3. Begin dislodging cork. • Move the lever arm down toward the neck of the bottle. Set the first set of ridges at the bottom of the lever arm on the lip of the bottle. Push down on the lever so that the cork begins moving upward. If necessary, use the second set of ridges on the lever arm to continue dislodging the cork. • Make sure you have a firm grip on the bottle, and that the lever arm is firmly in place, before you begin pulling up. Otherwise, the arm might slip. • If the cork won't budge, you may not have screwed the corkscrew in far enough. Twist it until there is only one twist remaining before using the lever. 4. Remove the cork • Pull up the handle of the sommelier knife's handle firmly. The cork should easily lift from the bottle with a slight pop. • If the cork doesn't lift from the bottle, screw the corkscrew in deeper, lift the cork using the lever arm, and try pulling on the...
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...A potential response is that one may proceed in Trolley but not in Transplant. The key difference can be explained by the Kantian idea of using people as an end in itself, rather than a means. In essence, for an agent to proceed in Transplant, he physically needs the body of a healthy man in order to save the five; whereas in Trolley the bystander does not use his victim in any sense (Thompson, Reading B). While this idea explains Trolley and Transplant in its vanilla form, it fails to explain the permissibility of pulling the lever in the loop variant (Thompson, Reading B) where one must be used or the five will die. The doctrine of double effect is a principle which states that an action which is morally impermissible if done intentionally, may be permissible if it only brought about as a foreseen consequence of promoting an ultimate good end (Study Guide p. 42). In the case of Transplant, the doctrine may explain the outcome of saving the five but fails to explain the means of doing so. If the organs were obtained by a means where the agent did not intentionally kill a person, then the doctrine may be able explain this. However in order to save the five, an agent must kill the one, and therefore it is implausible to state that the intentional murder of an innocent to achieve an end can be passed off as a foreseen consequence. Thompson’s explanation on the permissibility of proceeding in Trolley relates to the histories of how each person came to be where they are on each...
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...Hustler FasTrak Super Duty 48-60 Parts Manual ••••••• Excel Industries, Inc. ••••• P.O. Box 7000 ••• Hesston, Kansas • 67062-2097 WARNING: The engine exhaust from this product contains chemicals known to the State of California to cause cancer, birth defects or other reproductive harm. NOTICE OF REQUIREMENT OF SPARK ARRESTER MUFFLER This equipment may create sparks that can start fires around dry vegetation. California Public Resources Code Section 4442.6 provides that it is unlawful to use or operate an internal combustion engine on any forest-covered, brush-covered, or grass-covered land unless the engine is equipped with a spark arrester maintained in effective working order. A spark arrester is a device constructed of nonflammable materials specifically for the purpose of removing and retaining carbon and other flammable particles over 0.0232 of an inch in size from the exhaust flow of an internal combustion engine that uses hydrocarbon fuels or which is qualified and rated by the United States Forest Service. Other states or federal areas may have similar laws. The Operator Should Contact Local Fire Agencies For Laws or Regulations Relating to Fire Prevention Requirements. THIS EQUIPMENT DOES NOT HAVE A SPARK ARRESTER AND YOU SHOULD CONTACT YOUR AUTHORIZED DEALER FOR THE PURCHASE OF A SPARK ARRESTER. Inspect spark arrester daily; replace every 500 hours or as needed. The Engine Owner’s Manual provides information regarding the U.S. Environmental Protection Agency...
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...DATA AND RESULTS Diagram A Diagram B (Computation of the distance of F2) 48 cm = center T1= (F1) (d1) = (0.1kg) (9.8 m/s²) (0.38m) = 0.37 N-m T2= (F2) (d2) = (0.2kg) (9.8m/s²) (0.19m) = 0.37 N-m Torque 1 and Torque 2 are equal. Therefore, we are mathematically correct in diagram B. Diagram C (Computation of the weight of meter stick) T1= (F1) (d1) = (0.1kg) (9.8m/s²) (0.15m) = 0.147 N-m or 0.15 N-m T2= (F2) (d2) = (0.2kg) (9.8m/s²) (0.12m) = 0.2352 N-m or 0.24 N-m Torque 1 and 2 are not equal in mathematical method. Therefore, there were errors in balancing the two loads. APPLICATIONS A. Explain the condition below 1. It is much easier to carry a weight in your hand when your arm is at your side than it is when your arm is stretching out in front of you. Use the concept of torque to explain this effect. * When your arm is stretching out in front of you, any weight force exerted on your hand is at right angle to the lever arm between your shoulder and hand and produces a large torque above your shoulder. On the other hand, when your arm is at your side, any weight force exerted on your hand is directed away from your shoulder and produces no torque above your shoulder. B. Analyze the following situations. Show a diagram of the torque in each problem. Box your final answer. 1. A 15-kg child and a 25-kg child at ends of a 4m seesaw pivoted at its center. Where should a third child of 10...
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